How to Configure Pod initialization in a specific order in Kubernetes?

To create dependency among the deployment, there needs to be a sequence of certain condition true.

For example, Wait for the pod "busybox1" to contain the status condition of type "Ready".

kubectl wait --for=condition=Ready pod/busybox1

after that, you can roll out the next deployment.

For further detail see kubectl-wait

Here is an another example from @Michael Hausenblas job-dependencies, having dependencies among the job objects.

If you’d like to kick off another job after worker has completed? Here you go:

$ kubectl -n waitplayground \
             wait --for=condition=complete --timeout=32s \     
             job/worker
job.batch/worker condition met

It's possible to order the launch of initContainers in a Pod, or Pods that belong in the same StatefulSet. However, those solutions do not apply to your case.

This is because ordering initialization is not the standard approach for solving your issue. In a microservices architecture, and more specifically Kubernetes, you would write your containers such that they try to call the services they depend on (whether they are up or not) and if they aren't available, you let your containers crash. This works because Kubernetes provides a self-healing mechanism that automatically restarts containers if they fail. This way, your containers will try to connect to the services they depend on, and if the latter aren't available, the containers will crash and try again later using exponential back-off.

By removing unnecessary dependencies between services, you simplify the deployment of your application and reduce coupling between different services.